The design optimizations of a golf clubhead and a ball were performed with numerical experiments. The golf clubhead was designed for maximizing the flying distance of a golfball. The thickness distribution of the clubface, the shape of the clubhead and the mass distribution were set to be the design variables. Since the sensitivity function of this kind of problem is difficult to be derived, a non-sensitivity-based method called the basis vector method was used. The basis vectors were created by using eigenmodes obtained from modal analysis. Another numerical approach of Design of Experiment was used for the optimal design of a multi-piece golfball for maximizing the flying distance and improving the feeling at impact. In this optimization, the thickness and material properties of each layer were set as design variables. Numerical examples were provided to show the effectiveness of presented approach to the optimal design of golf clubhead and ball.